Transient nonlinear localization and beat phenomena are studied in a system of two rods coupled with a nonlinear backlash spring. The method of Karhunen-Loeve (K-L) decomposition is used to reduce the order of the dynamics, and to study nonlinear effects by considering energy transfers between leading K-L modes. The computed K-L modes are used to discretize the governing partial differential equations, thus creating accurate and computationally efficient low-dimensional nonlinear models of the system. Reconstruction of transient nonlinear responses using these low dimensional models reveals the accuracy of the order reduction. Poincare´ maps are utilized to study the nonlinear localization and beat phenomena caused by the clearance connecting the coupled rods.
Nonlinear Transient Localization and Beat Phenomena Due to Backlash in a Coupled Flexible System
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received Oct. 1999; revised Aug. 2000. Associate Editor: S. C. Sinha.
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Ma , X., and Vakakis, A. F. (August 1, 2000). "Nonlinear Transient Localization and Beat Phenomena Due to Backlash in a Coupled Flexible System ." ASME. J. Vib. Acoust. January 2001; 123(1): 36–44. https://doi.org/10.1115/1.1320813
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